You are given an instance of a problem where you have an n x n grid of squares. Each square can be unpainted or can have a hole, so you cannot go on the square with a hole. The objective is to paint all the squares that do not have a hole. You start in the square (0,0) which is unpainted. The actions you can do are: (1) paint the square you are on if it is not painted; (2) move, either vertically or horizontally, to an adjacent square inside the grid that is not painted and does not have a hole. a. Describe a state-space representation for the problem, specifying the state representation, the initial state, the goal condition, and the actions. b. Is the state space finite? Is it a tree or a graph? c. Propose a heuristic for the problem. Is your heuristics admissible or not? Explain briefly your answer
You are given an instance of a problem where you have an n x n grid of squares. Each square can be unpainted or can have a hole, so you cannot go on the square with a hole. The objective is to paint all the squares that do not have a hole. You start in the square (0,0) which is unpainted. The actions you can do are: (1) paint the square you are on if it is not painted; (2) move, either vertically or horizontally, to an adjacent square inside the grid that is not painted and does not have a hole. a. Describe a state-space representation for the problem, specifying the state representation, the initial state, the goal condition, and the actions. b. Is the state space finite? Is it a tree or a graph? c. Propose a heuristic for the problem. Is your heuristics admissible or not? Explain briefly your answer
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter17: Markov Chains
Section: Chapter Questions
Problem 12RP
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You are given an instance of a problem where you have an n x n grid
of squares. Each square can be unpainted or can have a hole, so you cannot go
on the square with a hole. The objective is to paint all the squares that do not
have a hole. You start in the square (0,0) which is unpainted. The actions you
can do are: (1) paint the square you are on if it is not painted; (2) move, either
vertically or horizontally, to an adjacent square inside the grid that is not painted
and does not have a hole.
a. Describe a state-space representation for the problem, specifying the
state representation, the initial state, the goal condition, and the actions.
b. Is the state space finite? Is it a tree or a graph?
c. Propose a heuristic for the problem. Is your heuristics admissible or not?
Explain briefly your answer
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